Edge Turbulence Research Articles

Nonlinear Dynamics in the Tokamak Edge

AbstractThe nonlinear character of the tokamak edge results from a unique combination of parameters, leading to a wide dynamical range for most processes. The energetically consistent gyrokinetic equilibrium is emphasised. Edge turbulence computed gyrokinetically exhibits energetic contact to mesoscale MHD and does not follow linear scaling. Gyrofluid studies show self consistent profiles, currents and flows which are kicked out of equilibrium to varying degree. L‐mode turbulence and ELM crash phenomenology are both examples of energetic contact between turbulence and MHD, with opposite causality. The overall equilibrium is a statistical saturation rather than a state to which the plasma dissipatively converges (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DNS of spark ignition and edge flame propagation in turbulent droplet-laden mixing layers

A parametric study of forced ignition at the mixing layer between air and air carrying fine monosized fuel droplets is done through one-step chemistry direct numerical simulations to determine the influence of the size and volatility of the droplets, the spark location, the droplet-air mixing layer initial thickness and the turbulence intensity on the ignition success and the subsequent flame propagation. The propagation is analyzed in terms of edge flame displacement speed, which has not been studied before for turbulent edge spray flames. Spark ignition successfully resulted in a tribrachial flame if enough fuel vapour was available at the spark location, which occurred when the local droplet number density was high. Ignition was achieved even when the spark was offset from the spray, on the air side, due to the diffusion of heat from the spark, provided droplets evaporated rapidly. Large kernels were obtained by sparking close to the spray, since fuel was more readily available. At long times after the spark, for all flames studied, the probability density function of the displacement speed was wide, with a mean value in the range 0.55–0.75SL, with SL the laminar burning velocity of a stoichiometric gaseous premixed flame. This value is close to the mean displacement speed in turbulent edge flames with gaseous fuel. The displacement speed was negatively correlated with curvature. The detrimental effect of curvature was attenuated with a large initial kernel and by increasing the thickness of the mixing layer. The mixing layer was thicker when evaporation was slow and the turbulence intensity higher. However, high turbulence intensity also distorted the kernel which could lead to high values of curvature. The edge flame reaction component increased when the maximum temperature coincided with the stoichiometric contour. The results are consistent with the limited available experimental evidence and provide insights into the processes associated with ignition of practical spray flames.

Resonant magnetic perturbation experiments on MAST using external and internal coils for ELM control

Experiments have been performed on MAST using both external (n = 1, 2) and internal (n = 3) resonant magnetic perturbation (RMP) coils. ELM suppression has not been achieved even though vacuum modelling shows that either set of coils can produce a region (ΔΨpol > 0.17), for which the Chirikov parameter is greater than 1, wider than that correlated with ELM suppression in DIII-D. Although complete ELM suppression has not been achieved, application of RMPs has triggered ELMs in ELM free H-mode periods (n = 3) and increased the ELM frequency in regularly ELM-ing discharges (n = 2, 3). In addition, the application of RMPs in an n = 3 configuration has produced large changes to the edge turbulence in L-mode discharges.

Lagrangian dynamics of drift-wave turbulence

The statistical properties of Lagrangian particle transport are investigated in dissipative drift-wave turbulence modelled by the Hasegawa–Wakatani system. By varying the adiabaticity parameter c , the flow regime can be modified from a hydrodynamic limit for c = 0 to a geostrophic limit for c → ∞ . For c of order unity the quasi-adiabatic regime is obtained, which might be relevant to describe the edge turbulence of fusion plasmas in tokamaks. This particularity of the model allows one to study the change in dynamics when varying from one turbulent flow regime to another. By means of direct numerical simulation we consider four values for c and show that the Lagrangian dynamics is most intermittent in the hydrodynamic regime, while the other regimes are not or only weakly intermittent. In both quasi-adiabatic and quasi-geostrophic regimes the PDFs of acceleration exhibit exponential tails. This behaviour is due to the pressure term in the acceleration and not a signature of intermittency.

Development of a High-Speed VUV Camera System for 2-Dimensional Imaging of Edge Turbulent Structure in the LHD

To clarify the role of edge turbulent transport, measurements of fluctuations with high temporal and spatial resolution are necessary. In this case, if 2-dimensional structures are observed, more detailed characteristics of edge turbulence can be clarified, since the propagation direction of the fluctuations and the mode number are directly visually studied. Therefore, a high-speed vacuum ultraviolet (VUV) camera system for 2-dimensional imaging of edge turbulent structures was developed and installed in the Large Helical Device (LHD). This optical system is composed of two multi-layer mirrors made of Mo/Si and a micro-channel plate (MCP). VUV emissions from plasmas are reflected at the multi-layer mirrors with high reflectivity and imaged on the MCP. The VUV emission of impurity carbon (n = 4-2 transition of C VI) near 13.5 nm can be observed with this system. In this paper, the components of this VUV camera system and the analytical method and calculations are described in detail. Moreover, preliminary results observed in the LHD are presented.

Saturation mechanisms for edge turbulence

Saturation mechanisms for two-dimensional (2D) edge turbulence are studied in a Braginskii-type fluid model using the scrape-off-layer turbulence code. The simulations study the interaction of edge and scrape-off-layer (SOL) turbulence, blob generation, momentum transport, and shear flow generation in 2D turbulence. It is shown that a key parameter is the zonal flow shear damping rate, which controls both the level of saturated turbulence and the rate of blob generation. The flow shear profile is produced by a combination of the turbulent Reynold’s stress inside the last closed surface and the sheath-induced flow in the SOL. The turbulent properties are studied as a function of zonal flow damping. The role of other edge and SOL dissipation mechanisms are also discussed.

Simulation of the generation of turbulence motion in edge wakes

The process of generating turbulence in edge wakes has been simulated and the results of the simulation are presented. The proposed mathematical model follows from a special procedure, which aims to average the flow parameters on scales comparable with the free path of molecules. The examined mechanism of generating turbulence is described by an expended set of Euler and Navier-Stokes nonstationary equations, with additional dispersive summands of the third order, which are obtained, if one uses the averaging procedure. The basic hydrodynamic equations are integrated by means of the well-known Godunov procedure of the second order. The calculated averaged performances of the turbulent flows agree with the experimental data.

Edge localized mode control experiments on MAST using resonant magnetic perturbations from in-vessel coils

Edge localized mode (ELM) control has been investigated on MAST with a set of in-vessel coils producing n = 3 perturbations. In spite of a broad enough region where the Chirikov parameter is above 1, according to the criterion employed for the design of the ITER ELM control coils, no effect was seen on type I ELMs. The behaviour on MAST is different from that in DIII-D in this respect. The coils do have an effect, however, on Ohmic L-mode plasmas and plasmas just above the L–H transition. In the former, they induce a density pump-out, modify the turbulence characteristics and edge radial electric field and produce a strike point splitting, while in the latter they can trigger ELMs in ELM-free plasmas.

Electron-cyclotron wave scattering by edge density fluctuations in ITER

The effect of edge turbulence on the electron-cyclotron wave propagation in ITER is investigated with emphasis on wave scattering, beam broadening, and its influence on localized heating and current drive. A wave used for electron-cyclotron current drive (ECCD) must cross the edge of the plasma, where density fluctuations can be large enough to bring on wave scattering. The scattering angle due to the density fluctuations is small, but the beam propagates over a distance of several meters up to the resonance layer and even small angle scattering leads to a deviation of several centimeters at the deposition location. Since the localization of ECCD is crucial for the control of neoclassical tearing modes, this issue is of great importance to the ITER design. The wave scattering process is described on the basis of a Fokker–Planck equation, where the diffusion coefficient is calculated analytically as well as computed numerically using a ray tracing code.

Dependence of the L- to H-mode power threshold on toroidal rotation and the link to edge turbulence dynamics

The injected power required to induce a transition from L-mode to H-mode plasmas is found to depend strongly on the injected neutral beam torque and consequent plasma toroidal rotation. Edge turbulence and flows, measured near the outboard midplane of the plasma (0.85 < r/a < 1.0) on DIII-D with the high-sensitivity 2D beam emission spectroscopy (BES) system, likewise vary with rotation and suggest a causative connection. The L–H power threshold in plasmas with the ion ∇B drift directed away from the X-point decreases from 4–6 MW with co-current beam injection, to 2–3 MW near zero net injected torque and to <2 MW with counter-injection in the discharges examined. Plasmas with the ion ∇B drift directed towards the X-point exhibit a qualitatively similar though less pronounced power threshold dependence on rotation. 2D edge turbulence measurements with BES show an increasing poloidal flow shear as the L–H transition is approached in all conditions. As toroidal rotation is varied from co-current to balanced in L-mode plasmas, the edge turbulence changes from a uni-modal character to a bi-modal structure, with the appearance of a low-frequency (f = 10–50 kHz) mode propagating in the electron diamagnetic direction, similar to what is observed as the ion ∇B drift is directed towards the X-point in co-rotating plasmas. At low rotation, the poloidal turbulence flow near the edge reverses prior to the L–H transition, generating a significant poloidal flow shear that exceeds the measured turbulence decorrelation rate. This increased poloidal turbulence velocity shear appears to facilitate the L–H transition. No such reversal is observed in high rotation plasmas. The high-frequency poloidal turbulence velocity spectrum exhibits a transition from a geodesic acoustic mode zonal flow to a higher-power, lower frequency zero-mean-frequency zonal flow as rotation varies from co-current to balanced during a torque scan at constant injected neutral beam power, perhaps also facilitating the L–H transition. This reduced power threshold at lower toroidal rotation may benefit inherently low-rotation plasmas such as ITER.

Edge turbulence characterization in RFX-mod with optical diagnostics

In the edge region of fusion devices coherent structures (blobs) are commonly observed. In order to investigate their evolution and the possible driving mechanisms, we studied the relationship between the size of the coherent structures and the local characteristic length Lp of the edge electron pressure profile Pe(r), together with the effect of magnetic fluctuations on ∇Pe. The results show an increase in the blob size with both Lp and magnetic fluctuations, suggesting an interplay between electron pressure gradient, magnetic fluctuations and edge turbulence generation.Measurements of the spatial scales of the edge turbulence structures and the corresponding toroidal phase velocity are obtained in the reversed field pinch RFX-mod by means of a gas puffing imaging diagnostic, while the local edge profiles of electron density ne(r) and temperature Te(r) and therefore Pe(r) have been measured via the line intensity ratio technique of helium emission lines.

Level-crossing function in the analysis of edge plasma turbulence

The amplitude variability of the confined fusion plasma turbulence is neglected in order to study solely its zero-crossing information. The retained zero-crossing set enables insight into various aspects of edge plasma turbulence. Certain common features with neutral fluid turbulence are recognized in the low confinement regime (L-mode). Spectral characteristics of the zero-crossing set are compared between L-mode, dithering H-mode and H-mode plasma edge turbulence and a scaling exponent characterizing the tendency of small scales to cluster is introduced. A transformation invariant level-crossing function is shown to be a more reliable indicator of stable equilibrium states than the probability density function. In particular the zero-crossing function detects L–H transitions and recognizes edge localized modes as catastrophic events in the sense of stochastic catastrophe theory. The method may be of significant importance in the analysis and control of edge plasma trubulence.

Edge turbulence measurements in electron-heated Helically Symmetric Experiment plasmas

This paper presents edge measurements utilizing Langmuir probes to characterize plasma turbulence in the Helically Symmetric Experiment (HSX) [F. S. B. Anderson et al., Fusion Technol. 27, 273 (1995)]. Normalized density and potential fluctuations exhibit strong intensities but are comparable to mixing length estimates using measured correlation lengths. The correlation lengths are isotropic with respect to radial and poloidal directions and follow local (gyro-Bohm) drift wave expectations. These observations are common to measurements in both the optimized quasihelically symmetric (QHS) configuration, as well as a configuration where the symmetry is degraded intentionally. The resulting turbulent particle flux in higher density QHS discharges is in good quantitative agreement with transport analysis using three-dimensional neutral gas simulations. The measured turbulence characteristics are compared to a quasilinear trapped electron mode (TEM) drift wave model [H. Nordman, J. Weiland, and A. Jarmén, Nucl. Fusion 30, 983 (1990)] that has been used to predict the anomalous transport in HSX. While quantitative differences exist (factors of 2–3), there is a general consistency between the turbulence measurements and the TEM drift wave model.

Particle-in-cell simulation with Vlasov ions and drift kinetic electrons

There are certain limitations in using gyrokinetic ions for simulations of turbulent transport in tokamak plasmas. Applications where Vlasov ions might be more appropriate include the electron temperature gradient driven turbulence, edge turbulence with steep density gradient, and magnetic reconnection in a weak guide field. In such cases the ion gyrokinetic model presently used in simulations needs to be extended, but a satisfactory extension valid for fully electromagnetic turbulence is not presently available. Even if an accurate model is found, its numerical implementation could be very challenging. We propose a kinetic model that combines Vlasov ions with gyrokinetic electrons to avoid the difficulties with gyrokinetic ions. The field equations of this model are the Faraday’s equation and the Ampere’s equation without the displacement current. The perturbed fields B1 and E1 rather than the scalar and vector potentials are used to formulate the field equations. We have devised an implicit scheme for this model, demonstrated in three-dimensional slab for the Alfvén waves, the drift Alfvén instability and the ion acoustic waves.

Fully electromagnetic nonlinear gyrokinetic equations for tokamak edge turbulence

An energy conserving set of the fully electromagnetic nonlinear gyrokinetic Vlasov equation and Maxwell’s equations, which is applicable to both L-mode turbulence with large amplitude and H-mode turbulence in the presence of high E×B shear has been derived. The phase-space action variational Lie perturbation method ensures the preservation of the conservation laws of the underlying Vlasov–Maxwell system. Generalized ordering takes ρi⪡ρθi∼LE∼Lp⪡R [here ρi is the thermal ion Larmor radius and ρθi=B∕(Bθρi)], as typically observed in the tokamak H-mode edge, with LE and Lp being the radial electric field and pressure gradient lengths. k⊥ρi∼1 is assumed for generality, and the relative fluctuation amplitudes eδϕ∕Ti∼δB∕B are kept up to the second order. Extending the electrostatic theory in the presence of high E×B shear [Hahm, Phys. Plasmas 3, 4658 (1996)], contributions of electromagnetic fluctuations to the particle charge density and current are explicitly evaluated via pullback transformation from the gyro...

Experimental Study of a Mach 3 Compression RampInteraction at Re{theta} = 2400

Experiments were performed to investigate the flow in a Mach 2.9 shock wave turbulent boundary-layer interaction at a Reynolds number based on momentum thickness of 2400. The flow configuration was a nominally two-dimensional 24 deg compression ramp, which exhibited a separation bubble in the corner region. Mean flow quantities, including the velocity profile upstream and downstream of the corner, and the wall pressure through the interaction were measured. Filtered Rayleigh scattering was used to visualize the flow structure in the interaction and provide quantitative measurements of the turbulent structure angle and the intermittency of the boundary-layer edge turbulence. The shock motion was characterized by measuring the fluctuating wall pressure. The results indicate that, compared to previous measurements obtained at higher Reynolds numbers of 60-80,000, the separation bubble is approximately twice as long, the root mean square of the wall-pressure fluctuations has a relatively smaller peak, and the intermittency of the wall-pressure signal in the shock-foot region is attenuated. As in the high-Reynolds-number case, the shock motion has a broadband frequency distribution with a peak slightly below 1 kHz. The mean flow quantities, root mean square wall-pressure-fluctuation profile, wall-pressure signal, and shock-motion frequency agree well with the direct numerical simulation of a previous study at matching conditions.

Edge turbulence scaling in RFX-mod as measured using GPI diagnostic

The nature of plasma edge turbulence has been studied in the Reversed Field Pinch (RFP) RFX-mod, making use of a Gas Puffing Imaging (GPI) diagnostic, with high time (2 MHz) and space (5 mm) resolution. The edge turbulence has been characterized in terms of toroidal phase velocity of fluctuations, v ϕ , of the width of emission structures, 2 σ, and of their linear density in the toroidal direction. The packing fraction ƒ p of intermittent structures has been estimated as the fraction of occupied area in a plane perpendicular to the magnetic field. The behaviors of v ϕ , ƒ p, and 2 σ are reported as functions of the density normalized to its Greenwald value, n/n G . A comparison at different plasma regimes of an effective diffusion coefficient D p due to the plasma trapped in coherent structures has been discussed. A decreasing trend of D p with n/n G values has been guessed.

Edge turbulence and SOL transport in tokamaks

Some key topics in tokamak edge plasma transport and turbulence are reviewed. Multi-device results reveal a new paradigm of scrape-off layer (SOL) transport. Radial transport is driven by intermittency throughout the SOL, in between edge localized modes (ELMs) in H-mode, and comprised of plasma filaments that are generated near the last closed flux surface likely by interchange instability. The filaments travel radially at speeds of ∼1 km/s into the SOL and have a poloidal size of 1–3 cm in most devices. The radial transport in the SOL is poloidally asymmetric, by factors of 2–5, causing a pressure peak in the low field side. This asymmetry and other neo-classical terms, such as Pfirsch–Schlüter currents, are found to drive strong SOL flows. The intermittent particle flux, is 20% of the total, including ELMs, at low collisionality, becoming 70% of total at high collisionality. Numerical and analytical models can reproduce the scaling of intermittency with collisionality as well as many details of the filament dynamics in the SOL.

Spatial structure of scrape-off-layer filaments near the midplane and X-point regions of Alcator-C-Mod

Movies of edge turbulence at both the outboard midplane and the region outboard of the typical lower X-point location in C-Mod have been obtained using gas-puff-imaging together with fast-framing cameras. Intermittent turbulence structures, typically referred to as blobs or filaments, are observed in both locations. Near the midplane the filaments are roughly circular in cross-section, while in the X-point region they are highly elongated. Filament velocities in this region are ∼3x faster than the radial velocities at the midplane, in a direction roughly outward across the local flux surfaces. The observations are consistent with the picture that the filaments arise in the outboard region and, as a consequence of the rapid parallel diffusion of the potential perturbations, map along field lines. Results from a 3D BOUT turbulence simulation reproduce many of the spatial features observed in the experiment.

Inter-ELM filaments and turbulent transport in the Mega-Amp Spherical Tokamak

Results on edge turbulence in periods separating edge localised modes (ELMs), i.e. inter-ELM periods, in Mega-Amp Spherical Tokamak (MAST) are presented. It is shown through combined measurements of fast camera images and reciprocating Langmuir probes that filamentary structures contribute to transport during these periods. Analysis of Dα light emission reveals that inter-ELM filaments are the lowest amplitude fluctuations in the MAST scrape-off layer (SOL) relative to L-mode and ELM filaments. Physical properties such as size, density and mode numbers have also been characterized, along with measurements of the spatio-temporal evolution: inter-ELM filaments are found to rotate in the vicinity of the last closed flux surface and propagate radially outwards. Motion of these filaments is found to depend strongly on plasma density such that with increasing density, there is an enhancement of the radial transport manifested by an increased number of filaments which leave the edge and travel faster into the SOL. Camera images show that intermittent fluctuations in ion saturation current signals correspond to inter-ELM filaments passing the probe. Measured radial e-folding lengths indicate larger decay lengths at higher densities. Similar trends are also obtained in simulations of a filament propagating radially and losing particles on ion parallel loss timescales. Finally, a discussion is presented on how the radial velocity and Isat measurements reported in this paper are used to test the velocity scalings predicted by different theories.